A brief History of Time: From Big Bang to Black Holes

particle can be regarded as a 0-brane and a string as a 1-brane but there
were also p-branes for p=2 to p=9.) What this seems to indicate is that there
is a sort of democracy among supergravity, string, and p-brane theories:
they seem to fit together but none can be said to be more fundamental than

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the others. They appear to be different approximations to some fundamental
theory that are valid in different situations.
People have searched for this underlying theory, but without any success
so far. However, I believe there may not be any single formulation of the
fundamental theory any more than, as Gödel showed, one could formulate
arithmetic in terms of a single set of axioms. Instead it may be like maps –
you can’t use a single map to describe the surface of the earth or an anchor
ring: you need at least two maps in the case of the earth and four for the
anchor ring to cover every point. Each map is valid only in a limited region,
but different maps will have a region of overlap. The collection of maps
provides a complete description of the surface. Similarly, in physics it may
be necessary to use different formulations in different situations, but two
different formulations would agree in situations where they can both be
applied. The whole collection of different formulations could be regarded as
a complete unified theory, though one that could not be expressed in terms
of a single set of postulates.
But can there really be such a unified theory? Or are we perhaps just
chasing a mirage? There seem to be three possibilities:
1) There really is a complete unified theory (or a collection of
overlapping formulations), which we will someday discover if we are smart
enough.
2) There is no ultimate theory of the universe, just an infinite sequence of
theories that describe the universe more and more accurately.
3) There is no theory of the universe: events cannot be predicted beyond
a certain extent but occur in a random and arbitrary manner.
Some would argue for the third possibility on the grounds that if there
were a complete set of laws, that would infringe on God’s freedom to
change his mind and intervene in the world. It’s a bit like the old paradox:
can God make a stone so heavy that he can’t lift it? But the idea that God
might want to change his mind is an example of the fallacy, pointed out by
St Augustine, of imagining God as a being existing in time: time is a
property only of the universe that God created. Presumably, he knew what
he intended when he set it up!
With the advent of quantum mechanics, we have come to recognize that
events cannot be predicted with complete accuracy but that there is always
a degree of uncertainty. If one likes, one could ascribe this randomness to
the intervention of God, but it would be a very strange kind of intervention:

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there is no evidence that it is directed toward any purpose. Indeed, if it
were, it would by definition not be random. In modern times, we have
effectively removed the third possibility above by redefining the goal of
science: our aim is to formulate a set of laws that enables us to predict
events only up to the limit set by the uncertainty principle.
The second possibility, that there is an infinite sequence of more and
more refined theories, is in agreement with all our experience so far. On
many occasions we have increased the sensitivity of our measurements or
made a new class of observations, only to discover new phenomena that
were not predicted by the existing theory, and to account for these we have
had to develop a more advanced theory. It would therefore not be very
surprising if the present generation of grand unified theories was wrong in
claiming that nothing essentially new will happen between the electroweak
unification energy of about 100 GeV and the grand unification energy of
about a thousand million million GeV. We might indeed expect to find
several new layers of structure more basic than the quarks and electrons that
we now regard as ‘elementary’ particles.
However, it seems that gravity may provide a limit to this sequence of
‘boxes within boxes.’ If one had a particle with an energy above what is
called the Planck energy, ten million million million GeV (1 followed by
nineteen zeros), its mass would be so concentrated that it would cut itself
off from the rest of the universe and form a little black hole. Thus it does
seem that the sequence of more and more refined theories should have some
limit as we go to higher and higher energies, so that there should be some
ultimate theory of the universe. Of course, the Planck energy is a very long
way from the energies of around a hundred GeV, which are the most that we
can produce in the laboratory at the present time. We shall not bridge that
gap with particle accelerators in the foreseeable future! The very early
stages of the universe, however, are an arena where such energies must
have occurred. I think that there is a good chance that the study of the early
universe and the requirements of mathematical consistency will lead us to a
complete unified theory within the lifetime of some of us who are around
today, always presuming we don’t blow ourselves up first.
What would it mean if we actually did discover the ultimate theory of the
universe? As was explained in 
Chapter 1
, we could never be quite sure that
we had indeed found the correct theory, since theories can’t be proved. But
if the theory was mathematically consistent and always gave predictions

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that agreed with observations, we could be reasonably confident that it was
the right one. It would bring to an end a long and glorious chapter in the
history of humanity’s intellectual struggle to understand the universe. But it
would also revolutionize the ordinary person’s understanding of the laws
that govern the universe. In Newton’s time it was possible for an educated
person to have a grasp of the whole of human knowledge, at least in outline.
But since then, the pace of the development of science has made this
impossible. Because theories are always being changed to account for new
observations, they are never properly digested or simplified so that ordinary
people can understand them. You have to be a specialist, and even then you
can only hope to have a proper grasp of a small proportion of the scientific
theories. Further, the rate of progress is so rapid that what one learns at
school or university is always a bit out of date. Only a few people can keep
up with the rapidly advancing frontier of knowledge, and they have to
devote their whole time to it and specialize in a small area. The rest of the
population has little idea of the advances that are being made or the
excitement they are generating. Seventy years ago, if Eddington is to be
believed, only two people understood the general theory of relativity.
Nowadays tens of thousands of university graduates do, and many millions
of people are at least familiar with the idea. If a complete unified theory
was discovered, it would only be a matter of time before it was digested and
simplified in the same way and taught in schools, at least in outline. We
would then all be able to have some understanding of the laws that govern
the universe and are responsible for our existence.
Even if we do discover a complete unified theory, it would not mean that
we would be able to predict events in general, for two reasons. The first is
the limitation that the uncertainty principle of quantum mechanics sets on
our powers of prediction. There is nothing we can do to get around that. In
practice, however, this first limitation is less restrictive than the second one.
It arises from the fact that we could not solve the equations of the theory
exactly, except in very simple situations. (We cannot even solve exactly for
the motion of three bodies in Newton’s theory of gravity, and the difficulty
increases with the number of bodies and the complexity of the theory.) We
already know the laws that govern the behavior of matter under all but the
most extreme conditions. In particular, we know the basic laws that underlie
all of chemistry and biology. Yet we have certainly not reduced these
subjects to the status of solved problems: we have, as yet, had little success

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in predicting human behavior from mathematical equations! So even if we
do find a complete set of basic laws, there will still be in the years ahead the
intellectually challenging task of developing better approximation methods,
so that we can make useful predictions of the probable outcomes in
complicated and realistic situations. A complete, consistent, unified theory
is only the first step: our goal is a complete understanding of the events
around us, and of our own existence.

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12
CONCLUSION
WE FIND OURSELVES
in a bewildering world. We want to make sense of what
we see around us and to ask: what is the nature of the universe? What is our
place in it and where did it and we come from? Why is it the way it is?
To try to answer these questions we adopt some ‘world picture.’ Just as
an infinite tower of tortoises supporting the flat earth is such a picture, so is
the theory of superstrings. Both are theories of the universe, though the
latter is much more mathematical and precise than the former. Both theories
lack observational evidence: no one has ever seen a giant tortoise with the
earth on its back, but then, no one has seen a superstring either. However,
the tortoise theory fails to be a good scientific theory because it predicts that
people should be able to fall off the edge of the world. This has not been
found to agree with experience, unless that turns out to be the explanation
for the people who are supposed to have disappeared in the Bermuda
Triangle!
The earliest theoretical attempts to describe and explain the universe
involved the idea that events and natural phenomena were controlled by
spirits with human emotions who acted in a very humanlike and
unpredictable manner. These spirits inhabited natural objects, like rivers and
mountains, including celestial bodies, like the sun and moon. They had to
be placated and their favors sought in order to ensure the fertility of the soil
and the rotation of the seasons. Gradually, however, it must have been
noticed that there were certain regularities: the sun always rose in the east
and set in the west, whether or not a sacrifice had been made to the sun god.
Further, the sun, the moon, and the planets followed precise paths across the
sky that could be predicted in advance with considerable accuracy. The sun
and the moon might still be gods, but they were gods who obeyed strict

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laws, apparently without any exceptions, if one discounts stories like that of
the sun stopping for Joshua.
At first, these regularities and laws were obvious only in astronomy and a
few other situations. However, as civilization developed, and particularly in
the last 300 years, more and more regularities and laws were discovered.
The success of these laws led Laplace at the beginning of the nineteenth
century to postulate scientific determinism; that is, he suggested that there
would be a set of laws that would determine the evolution of the universe
precisely, given its configuration at one time.
Laplace’s determinism was incomplete in two ways. It did not say how
the laws should be chosen and it did not specify the initial configuration of
the universe. These were left to God. God would choose how the universe
began and what laws it obeyed, but he would not intervene in the universe
once it had started. In effect, God was confined to the areas that nineteenth-
century science did not understand.
We now know that Laplace’s hopes of determinism cannot be realized, at
least in the terms he had in mind. The uncertainty principle of quantum
mechanics implies that certain pairs of quantities, such as the position and
velocity of a particle, cannot both be predicted with complete accuracy.
Quantum mechanics deals with this situation via a class of quantum theories
in which particles don’t have well-defined positions and velocities but are
represented by a wave. These quantum theories are deterministic in the
sense that they give laws for the evolution of the wave with time. Thus if
one knows the wave at one time, one can calculate it at any other time. The
unpredictable, random element comes in only when we try to interpret the
wave in terms of the positions and velocities of particles. But maybe that is
our mistake: maybe there are no particle positions and velocities, but only
waves. It is just that we try to fit the waves to our preconceived ideas of
positions and velocities. The resulting mismatch is the cause of the apparent
unpredictability.
In effect, we have redefined the task of science to be the discovery of
laws that will enable us to predict events up to the limits set by the
uncertainty principle. The question remains, however: how or why were the
laws and the initial state of the universe chosen?
In this book I have given special prominence to the laws that govern
gravity, because it is gravity that shapes the large-scale structure of the
universe, even though it is the weakest of the four categories of forces. The

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laws of gravity were incompatible with the view held until quite recently
that the universe is unchanging in time: the fact that gravity is always
attractive implies that the universe must be either expanding or contracting.
According to the general theory of relativity, there must have been a state of
infinite density in the past, the big bang, which would have been an
effective beginning of time. Similarly, if the whole universe recollapsed,
there must be another state of infinite density in the future, the big crunch,
which would be an end of time. Even if the whole universe did not
recollapse, there would be singularities in any localized regions that
collapsed to form black holes. These singularities would be an end of time
for anyone who fell into the black hole. At the big bang and other
singularities, all the laws would have broken down, so God would still have
had complete freedom to choose what happened and how the universe
began.
When we combine quantum mechanics with general relativity, there
seems to be a new possibility that did not arise before: that space and time
together might form a finite, four-dimensional space without singularities or
boundaries, like the surface of the earth but with more dimensions. It seems
that this idea could explain many of the observed features of the universe,
such as its large-scale uniformity and also the smaller-scale departures from
homogeneity, like galaxies, stars, and even human beings. It could even
account for the arrow of time that we observe. But if the universe is
completely self-contained, with no singularities or boundaries, and
completely described by a unified theory, that has profound implications for
the role of God as Creator.
Einstein once asked the question: ‘How much choice did God have in
constructing the universe?’ If the no boundary proposal is correct, he had no
freedom at all to choose initial conditions. He would, of course, still have
had the freedom to choose the laws that the universe obeyed. This, however,
may not really have been all that much of a choice; there may well be only
one, or a small number, of complete unified theories, such as the heterotic
string theory, that are self-consistent and allow the existence of structures as
complicated as human beings who can investigate the laws of the universe
and ask about the nature of God.
Even if there is only one possible unified theory, it is just a set of rules
and equations. What is it that breathes fire into the equations and makes a
universe for them to describe? The usual approach of science of

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constructing a mathematical model cannot answer the questions of why
there should be a universe for the model to describe. Why does the universe
go to all the bother of existing? Is the unified theory so compelling that it
brings about its own existence? Or does it need a creator, and, if so, does he
have any other effect on the universe? And who created him?
Up to now, most scientists have been too occupied with the development
of new theories that describe what the universe is to ask the question why.
On the other hand, the people whose business it is to ask why, the
philosophers, have not been able to keep up with the advance of scientific
theories. In the eighteenth century, philosophers considered the whole of
human knowledge, including science, to be their field and discussed
questions such as: did the universe have a beginning? However, in the
nineteenth and twentieth centuries, science became too technical and
mathematical for the philosophers, or anyone else except a few specialists.
Philosophers reduced the scope of their inquiries so much that Wittgenstein,
the most famous philosopher of this century, said, ‘The sole remaining task
for philosophy is the analysis of language.’ What a comedown from the
great tradition of philosophy from Aristotle to Kant!
However, if we do discover a complete theory, it should in time be
understandable in broad principle by everyone, not just a few scientists.
Then we shall all, philosophers, scientists, and just ordinary people, be able
to take part in the discussion of the question of why it is that we and the
universe exist. If we find the answer to that, it would be the ultimate
triumph of human reason – for then we would know the mind of God.

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ALBERT EINSTEIN
EINSTEIN’S CONNECTION WITH THE POLITICS OF THE
nuclear bomb is well
known: he signed the famous letter to President Franklin Roosevelt that
persuaded the United States to take the idea seriously, and he engaged in
postwar efforts to prevent nuclear war. But these were not just the isolated
actions of a scientist dragged into the world of politics. Einstein’s life was,
in fact, to use his own words, ‘divided between politics and equations.’
Einstein’s earliest political activity came during the First World War,
when he was a professor in Berlin. Sickened by what he saw as the waste of
human lives, he became involved in antiwar demonstrations. His advocacy
of civil disobedience and public encouragement of people to refuse
conscription did little to endear him to his colleagues. Then, following the
war, he directed his efforts toward reconciliation and improving
international relations. This, too, did not make him popular, and soon his
politics were making it difficult for him to visit the United States, even to
give lectures.
Einstein’s second great cause was Zionism. Although he was Jewish by
descent, Einstein rejected the biblical idea of God. However, a growing
awareness of anti-Semitism, both before and during the First World War,
led him gradually to identify with the Jewish community, and later to
become an outspoken supporter of Zionism. Once more unpopularity did
not stop him from speaking his mind. His theories came under attack; an
anti-Einstein organization was even set up. One man was convicted of
inciting others to murder Einstein (and fined a mere six dollars). But
Einstein was phlegmatic. When a book was published entitled 100 Authors